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A210870 Triangle of coefficients of polynomials u(n,x) jointly generated with A210871; see the Formula section. 3
1, 1, 1, 1, 2, 2, 1, 3, 3, 3, 1, 4, 6, 5, 5, 1, 5, 8, 12, 8, 8, 1, 6, 12, 17, 23, 13, 13, 1, 7, 15, 29, 33, 43, 21, 21, 1, 8, 20, 38, 64, 63, 79, 34, 34, 1, 9, 24, 56, 86, 136, 117, 143, 55, 55, 1, 10, 30, 70, 140, 187, 279, 214, 256, 89, 89, 1, 11, 35, 95, 180, 332 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

In row n, for n>1, the first two terms are 1 and n-1, and the last two are F(n) and F(n), where F = A000045 (Fibonacci numbers).

Row sums: A000975

Alternating row sums:  A113954

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..72.

FORMULA

u(n,x)=u(n-1,x)+x*v(n-1,x),

v(n,x)=(x+1)*u(n-1,x)+(x-1)*v(n-1,x)+1,

where u(1,x)=1, v(1,x)=1.

EXAMPLE

First six rows:

1

1...1

1...2...2

1...3...3...3

1...4...6...5....5

1...5...8...12...8...8

First three polynomials u(n,x): 1, 1 + x, 1 + 2x + 2x^2.

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 14;

u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];

v[n_, x_] := (x + 1)*u[n - 1, x] + (x - 1)*v[n - 1, x] + 1;

Table[Expand[u[n, x]], {n, 1, z/2}]

Table[Expand[v[n, x]], {n, 1, z/2}]

cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

TableForm[cu]

Flatten[%]    (* A210870 *)

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%]    (* A210871 *)

Table[u[n, x] /. x -> 1, {n, 1, z}]  (* A000975 *)

Table[v[n, x] /. x -> 1, {n, 1, z}]  (* A001045 *)

Table[u[n, x] /. x -> -1, {n, 1, z}]   (* A113954 *)

Table[v[n, x] /. x -> -1, {n, 1, z}]  (* A077925 *)

CROSSREFS

Cf. A210871, A208510.

Sequence in context: A117915 A294453 A097094 * A104726 A194195 A164999

Adjacent sequences:  A210867 A210868 A210869 * A210871 A210872 A210873

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 29 2012

STATUS

approved

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Last modified October 22 12:47 EDT 2019. Contains 328318 sequences. (Running on oeis4.)